Make the main ring wall (The wall between the lane and the inner ring) Impassable so no-one can jump over it, but keep smaller walls (like the wall between top tower and the health relic) passable, since the only champion that can really jump the big walls is kassadin anyway.

See pic

Red = Non jumpable wall
Green = Ok Wall.

Attached Thumbnails

 

Does the game have the capability to make walls non-jumpable, or would that require thickening of the walls?

This would make all the pathways waaay too small the size that the walls would have to be is just too big. They'd have to be bigger then the wall/area between the summoner platform and the lane, and that's a pretty big area.

Or you could just kill Kass... Focus him, get some MR, play champs that have cc...

This solution won't work.
Here is a solution that will work.

Limit Kassadin to his actual range of his ultimate cast. What am I talking about? He can rift walk further than it tells you he can.

Perfect example: http://i.imgur.com/Zhlst.jpg

I'm standing on the wall, the range is obviously not enough, but I can still jump over the wall. (Red: Cast range, Yellow: Projected cast range).

Ezreal can do this too, but not nearly to the extent that Kassadin can. Kassadin can jump over ANY wall in Dominion if positioned right.

Perhaps just allow it. Make a longer cooldown for it and make it require more mana.